Symbols "R" Us: Seismic imaging, one-way wave equations, pseudodifferential operators, path integrals, and all that Jazz

Ojenie Artoun, Diana David-Rus, Matthew Emmett, Lou Fishman, Sandra Fital, Chad M. Hogan, Jisun Lim, Enkeleida Lushi, Vesselin Marinov

In this report we summarize an extension of Fourier analysis for the solution of the wave equation with a non-constant coefficient corresponding to an inhomogeneous medium. The underlying physics of the problem is exploited to link pseudodifferential operators and phase space path integrals to obtain a marching algorithm that incorporates the backward scattering into the evolution of the wave. This allows us to successfully apply single-sweep, one-way marching methods in inherently two-way environments, which was not achieved before through other methods for this problem.